The term servo feedback implies the use of an active integrator within a negative feedback loop coupled from the output to the input of an amplifier system. In the most basic configuration, an integrator comprises a high-gain differential amplifier provided with capacitive feedback connected between its output and inverting input. The non-inverting input is coupled to a reference potential, while a sampling resistor connects between the main output node and the inverting input of the main differential amplifier, so that the integrator produces an output that represents the inverse of the time-integral of the difference between the main amplifier's output signal and the reference potential. The gain of such an integrator circuit will approach the open loop gain of the embedded differential amplifier for DC signals and will fall off at, for example, 6 dB per octave as the frequency increases.
The output signal from the integrator may be used directly as the negative servo feedback signal, or it may control means that provide the necessary feedback signal. Since the magnitude of the servo feedback falls off with increasing frequency, the effective closed loop gain of the amplifier system will increase with frequency until an asymptotic value is reached where the gain for AC signals will be equal to the nominal closed loop gain of the amplifier system, as determined in the normal fashion. It is therefore seen that the application of negative servo feedback around an amplifier system will impart a high-pass characteristic to its overall transfer function. In addition, since the servo loop operates to force the amplifier's output to maintain an average value of DC ground, the residual AC signal appearing at the amplifier's output will appear centered about the local common potential, thereby maximizing the useful dynamic range of the amplifier system.
Routine measurement of AC impedance is becoming an important part of testing protocols for electrochemical devices, especially in backup power systems where an unexpected component failure can have serious (sometimes fatal) consequences. In these applications, information derived from impedance trends is used to identify aging battery cells and schedule their replacement before failure occurs. However, obtaining reliable impedance data under field conditions, which usually involves man-portable, battery-powered test equipment, presents two unique challenges.
First, electrochemical cells possess a substantial DC bias that must be nulled out in order to allow efficient amplification of the AC response. Although the introduction of current mode servo feedback (e.g., U.S. Pat. No. 7,253,680) provided one approach to this problem, it failed to address the related problem of DC offsets arising from the test equipment itself.
Second, the total impedance of a battery cell can be extremely low—in some cases ≦0.1 mΩ. Hence, even an input signal of 2 amps AC (close to the upper limit available from portable equipment) may yield a response of 0.1 mV AC or less. In order to achieve adequate signal-to-noise ratios (a particular concern when measurements are made in the presence of RF interference), the response must be averaged over very many cycles and can require unreasonably long periods of time per measurement.
Therefore, what is needed is a method for testing battery networks that can be applied while the batteries are in operation, that takes into account both individual and overall battery health, and that can make adjustments for the needs of a particular application.